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Different kinds of two-parameter martingales

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Abstract

This paper is devoted to the study of all the different classes of two-parameter martingales which were introduced during the last decade. The problem of the relations between these classes is completely solved under the F-4 assumption and counter-examples are given in order to point out the differences between these classes. Characterizations in terms of Doob-Meyer-Cairoli decompositions are obtained. In the case where the filtration is generated by a two-parameter Poisson process, we prove that the class of strong martingales coincides with the class of martingales of direction independent variation.

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Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, 52100, Ramat Gan, Israel

    Ely Merzbach & David Nualart

  2. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Ely Merzbach & David Nualart

Authors
  1. Ely Merzbach
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  2. David Nualart
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Additional information

This work was carried out while the second author was a visitor at Bar-Ilan University.

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Merzbach, E., Nualart, D. Different kinds of two-parameter martingales. Israel J. Math. 52, 193–208 (1985). https://doi.org/10.1007/BF02786515

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  • DOI: https://doi.org/10.1007/BF02786515

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